State the first law of thermodynamics. Write the mathematical expression for it.

The first law of thermodynamics, also known as the law of energy conservation, is a fundamental principle in physics and thermodynamics. It states that energy cannot be created or destroyed in an isolated system; instead, it can only change forms or be transferred from one part of the system to another. In other words, the total energy of an isolated system remains constant over time.

Mathematically, the first law of thermodynamics can be expressed as:

ΔU = Q - W

Where:

ΔU represents the change in the internal energy of the system.
Q represents the heat added to the system.
W represents the work done by the system on its surroundings (or vice versa, depending on the sign convention).
This equation essentially states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings (or vice versa). It is a fundamental principle that governs the behavior of energy in thermodynamic processes.